#ifndef __Vector3_h___
#define __Vector3_h___

#include "Maths.h"
#include "Quaternion.h"



namespace MyCommon
{
	
	/** Standard 3-dimensional vector.
	@remarks
		A direction in 3D space represented as distances along the 3
		orthogonal axes (x, y, z). Note that positions, directions and
		scaling factors can be represented by a vector, depending on how
		you interpret the values.
	*/
	class Vector3
	{
	public:
		Real x, y, z;

		inline Vector3() : x(0),y(0),z(0) {}
		inline Vector3( const Real fX, const Real fY, const Real fZ )
			: x( fX ), y( fY ), z( fZ ){}
		inline explicit Vector3( const Real afCoordinate[3] )
			: x( afCoordinate[0] ),y( afCoordinate[1] ),z( afCoordinate[2] ){}
		inline explicit Vector3( const int afCoordinate[3] )
		{
			x = (Real)afCoordinate[0];
			y = (Real)afCoordinate[1];
			z = (Real)afCoordinate[2];
		}

		inline explicit Vector3( Real* const r )
			: x( r[0] ), y( r[1] ), z( r[2] ) {}

		inline explicit Vector3( const Real scaler )
			: x( scaler ), y( scaler ), z( scaler ){}

		inline Vector3( const Vector3& rkVector )
			: x( rkVector.x ), y( rkVector.y ), z( rkVector.z ){}

		inline Real operator [] ( const size_t i ) const
		{	assert( i < 3 );	return *(&x+i);	}

		inline Real& operator [] ( const size_t i )
		{	assert( i < 3 );	return *(&x+i);	}

		/// Pointer accessor for direct copying
		inline Real* ptr(){	return &x;}

		/// Pointer accessor for direct copying
		inline const Real* ptr() const {	return &x;	}

		/** Assigns the value of the other vector.
		@param
			rkVector The other vector
		*/
		inline Vector3& operator = ( const Vector3& rkVector )
		{
			x = rkVector.x;
			y = rkVector.y;
			z = rkVector.z;
			return *this;
		}

		inline Vector3& operator = ( const Real fScaler )
		{
			x = fScaler;
			y = fScaler;
			z = fScaler;
			return *this;
		}

		inline bool operator == ( const Vector3& rkVector ) const
		{	return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );	}

		inline bool operator != ( const Vector3& rkVector ) const
		{	return ( x != rkVector.x || y != rkVector.y || z != rkVector.z );	}

		inline Vector3 operator + ( const Vector3& rkVector ) const
		{	return Vector3(x + rkVector.x,y + rkVector.y,z + rkVector.z);	}

		inline Vector3 operator - ( const Vector3& rkVector ) const
		{	return Vector3(x - rkVector.x,y - rkVector.y,z - rkVector.z);	}

		inline Vector3 operator * ( const Real fScalar ) const
		{	return Vector3(x * fScalar,y * fScalar,z * fScalar);	}

		inline Vector3 operator * ( const Vector3& rhs) const
		{	return Vector3(x * rhs.x,y * rhs.y,z * rhs.z);	}

		inline Vector3 operator / ( const Real fScalar ) const
		{	
			assert( fScalar != 0.0 );
			Real fInv = 1.0 / fScalar;
			return Vector3(x * fInv,y * fInv,z * fInv);
		}

		inline Vector3 operator / ( const Vector3& rhs) const
		{	return Vector3(x / rhs.x,y / rhs.y,z / rhs.z);	}

		inline const Vector3& operator + () const
		{	return *this;	}

		inline Vector3 operator - () const
		{	return Vector3(-x, -y, -z);		}

		inline friend Vector3 operator * ( const Real fScalar, const Vector3& rkVector )
		{	return Vector3(fScalar * rkVector.x,fScalar * rkVector.y,fScalar * rkVector.z);	}

		inline friend Vector3 operator / ( const Real fScalar, const Vector3& rkVector )
		{	return Vector3(fScalar / rkVector.x,fScalar / rkVector.y,fScalar / rkVector.z);	}

		inline friend Vector3 operator + (const Vector3& lhs, const Real rhs)
		{	return Vector3(lhs.x + rhs,lhs.y + rhs,lhs.z + rhs);	}

		inline friend Vector3 operator + (const Real lhs, const Vector3& rhs)
		{	return Vector3(lhs + rhs.x,lhs + rhs.y,lhs + rhs.z);	}

		inline friend Vector3 operator - (const Vector3& lhs, const Real rhs)
		{	return Vector3(lhs.x - rhs,lhs.y - rhs,lhs.z - rhs);	}

		inline friend Vector3 operator - (const Real lhs, const Vector3& rhs)
		{	return Vector3(lhs - rhs.x,lhs - rhs.y,lhs - rhs.z);	}

		inline Vector3& operator += ( const Vector3& rkVector )
		{	x += rkVector.x;	y += rkVector.y;	z += rkVector.z;	return *this;}

		inline Vector3& operator += ( const Real fScalar )
		{	x += fScalar; y += fScalar; z += fScalar;	return *this;	}

		inline Vector3& operator -= ( const Vector3& rkVector )
		{	x -= rkVector.x; y -= rkVector.y; z -= rkVector.z; return *this; }

		inline Vector3& operator -= ( const Real fScalar )
		{	x -= fScalar; y -= fScalar; z -= fScalar; return *this; }

		inline Vector3& operator *= ( const Real fScalar )
		{	x *= fScalar; y *= fScalar; z *= fScalar; return *this; }

		inline Vector3& operator *= ( const Vector3& rkVector )
		{	x *= rkVector.x; y *= rkVector.y; z *= rkVector.z; return *this; }

		inline Vector3& operator /= ( const Real fScalar )
		{
			assert( fScalar != 0.0 );
			Real fInv = 1.0 / fScalar;
			x *= fInv;
			y *= fInv;
			z *= fInv;
			return *this;
		}

		inline Vector3& operator /= ( const Vector3& rkVector )
		{
			x /= rkVector.x;
			y /= rkVector.y;
			z /= rkVector.z;
			return *this;
		}

		/** truncates a vector so that its length does not exceed max
		@returns
			the previous length of the vector
		*/
		Real truncate(Real max)
		{
			Real len = length();
			if(len>max)
			{
				this->normalize();
				*this *= max;
				return max;
			}
			return len;
		}

		/** Returns the length (magnitude) of the vector.
		@warning
			This operation requires a square root and is expensive in
			terms of CPU operations. If you don't need to know the exact
			length (e.g. for just comparing lengths) use squaredLength()
			instead.
		*/
		inline Real length () const
		{	return Math::Sqrt( x * x + y * y + z * z );	}

		/** Returns the square of the length(magnitude) of the vector.
		@remarks
			This  method is for efficiency - calculating the actual
			length of a vector requires a square root, which is expensive
			in terms of the operations required. This method returns the
			square of the length of the vector, i.e. the same as the
			length but before the square root is taken. Use this if you
			want to find the longest / shortest vector without incurring
			the square root.
		*/
		inline Real squaredLength () const { return x * x + y * y + z * z; }

		/** Returns the distance to another vector.
		@warning
			This operation requires a square root and is expensive in
			terms of CPU operations. If you don't need to know the exact
			distance (e.g. for just comparing distances) use squaredDistance()
			instead.
		*/
		inline Real distance(const Vector3& rhs) const
		{	return (*this - rhs).length();	}

		/** Returns the square of the distance to another vector.
		@remarks
			This method is for efficiency - calculating the actual
			distance to another vector requires a square root, which is
			expensive in terms of the operations required. This method
			returns the square of the distance to another vector, i.e.
			the same as the distance but before the square root is taken.
			Use this if you want to find the longest / shortest distance
			without incurring the square root.
		*/
		inline Real squaredDistance(const Vector3& rhs) const
		{	return (*this - rhs).squaredLength();	}

		/** Calculates the dot (scalar) product of this vector with another.
		@remarks
			The dot product can be used to calculate the angle between 2
			vectors. If both are unit vectors, the dot product is the
			cosine of the angle; otherwise the dot product must be
			divided by the product of the lengths of both vectors to get
			the cosine of the angle. This result can further be used to
			calculate the distance of a point from a plane.
		@param
			vec Vector with which to calculate the dot product (together
			with this one).
		@returns
			A float representing the dot product value.
		*/
		inline Real dotProduct(const Vector3& vec) const
		{	return x * vec.x + y * vec.y + z * vec.z;	}

		/** Calculates the absolute dot (scalar) product of this vector with another.
		@remarks
			This function work similar dotProduct, except it use absolute value
			of each component of the vector to computing.
		@param
			vec Vector with which to calculate the absolute dot product (together
			with this one).
		@returns
			A Real representing the absolute dot product value.
		*/
		inline Real absDotProduct(const Vector3& vec) const
		{
			return Math::Abs(x * vec.x) + Math::Abs(y * vec.y) + Math::Abs(z * vec.z);
		}

		/** Normalizes the vector.
		@remarks
			This method normalizes the vector such that it's
			length / magnitude is 1. The result is called a unit vector.
		@note
			This function will not crash for zero-sized vectors, but there
			will be no changes made to their components.
		@returns The previous length of the vector.
		*/
		inline Real normalize()
		{
			Real fLength = Math::Sqrt( x * x + y * y + z * z );

			// Will also work for zero-sized vectors, but will change nothing
			if ( fLength > 1e-08 )
			{
				Real fInvLength = 1.0 / fLength;
				x *= fInvLength;
				y *= fInvLength;
				z *= fInvLength;
			}
			return fLength;
		}

		/** Calculates the cross-product of 2 vectors, i.e. the vector that
			lies perpendicular to them both.
		@remarks
			The cross-product is normally used to calculate the normal
			vector of a plane, by calculating the cross-product of 2
			non-equivalent vectors which lie on the plane (e.g. 2 edges
			of a triangle).
		@param
			vec Vector which, together with this one, will be used to
			calculate the cross-product.
		@returns
			A vector which is the result of the cross-product. This
			vector will <b>NOT</b> be normalised, to maximise efficiency
			- call Vector3::normalise on the result if you wish this to
			be done. As for which side the resultant vector will be on, the
			returned vector will be on the side from which the arc from 'this'
			to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z)
			= UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X.
			This is because OGRE uses a right-handed coordinate system.
		@par
			For a clearer explanation, look a the left and the bottom edges
			of your monitor's screen. Assume that the first vector is the
			left edge and the second vector is the bottom edge, both of
			them starting from the lower-left corner of the screen. The
			resulting vector is going to be perpendicular to both of them
			and will go <i>inside</i> the screen, towards the cathode tube
			(assuming you're using a CRT monitor, of course).
		*/
		inline Vector3 crossProduct( const Vector3& rkVector ) const
		{
			return Vector3(
				y * rkVector.z - z * rkVector.y,
				z * rkVector.x - x * rkVector.z,
				x * rkVector.y - y * rkVector.x);
		}

		/** Returns a vector at a point half way between this and the passed
			in vector.
		*/
		inline Vector3 midPoint( const Vector3& vec ) const
		{
			return Vector3(
				( x + vec.x ) * 0.5,
				( y + vec.y ) * 0.5,
				( z + vec.z ) * 0.5 );
		}

		/** Returns true if the vector's scalar components are all greater
			that the ones of the vector it is compared against.
		*/
		inline bool operator < ( const Vector3& rhs ) const
		{
			if( x < rhs.x && y < rhs.y && z < rhs.z )
				return true;
			return false;
		}

		/** Returns true if the vector's scalar components are all smaller
			that the ones of the vector it is compared against.
		*/
		inline bool operator > ( const Vector3& rhs ) const
		{
			if( x > rhs.x && y > rhs.y && z > rhs.z )
				return true;
			return false;
		}

		/** Sets this vector's components to the minimum of its own and the
			ones of the passed in vector.
		@remarks
			'Minimum' in this case means the combination of the lowest
			value of x, y and z from both vectors. Lowest is taken just
			numerically, not magnitude, so -1 < 0.
		*/
		inline void makeFloor( const Vector3& cmp )
		{
			if( cmp.x < x ) x = cmp.x;
			if( cmp.y < y ) y = cmp.y;
			if( cmp.z < z ) z = cmp.z;
		}

		/** Sets this vector's components to the maximum of its own and the
			ones of the passed in vector.
		@remarks
			'Maximum' in this case means the combination of the highest
			value of x, y and z from both vectors. Highest is taken just
			numerically, not magnitude, so 1 > -3.
		*/
		inline void makeCeil( const Vector3& cmp )
		{
			if( cmp.x > x ) x = cmp.x;
			if( cmp.y > y ) y = cmp.y;
			if( cmp.z > z ) z = cmp.z;
		}

		/** Generates a vector perpendicular to this vector (eg an 'up' vector).
		@remarks
			This method will return a vector which is perpendicular to this
			vector. There are an infinite number of possibilities but this
			method will guarantee to generate one of them. If you need more
			control you should use the Quaternion class.
		*/
		inline Vector3 perpendicular(void) const
		{
			static const Real fSquareZero = 1e-06 * 1e-06;
			Vector3 perp = this->crossProduct( Vector3::UNIT_X );

			// Check length
			if( perp.squaredLength() < fSquareZero )
			{
				/* This vector is the Y axis multiplied by a scalar, so we have
					to use another axis.
				*/
				perp = this->crossProduct( Vector3::UNIT_Y );
			}
			perp.normalize();
			return perp;
		}

		/** Generates a new random vector which deviates from this vector by a
			given angle in a random direction.
		@remarks
			This method assumes that the random number generator has already
			been seeded appropriately.
		@param
			angle The angle at which to deviate
		@param
			up Any vector perpendicular to this one (which could generated
			by cross-product of this vector and any other non-colinear
			vector). If you choose not to provide this the function will
			derive one on it's own, however if you provide one yourself the
			function will be faster (this allows you to reuse up vectors if
			you call this method more than once)
		@returns
			A random vector which deviates from this vector by angle. This
			vector will not be normalised, normalise it if you wish
			afterwards.
		*/
		inline Vector3 randomDeviant(
			const Radian& angle,
			const Vector3& up = Vector3::ZERO ) const
		{
			Vector3 newUp;

			if (up == Vector3::ZERO)
			{
				// Generate an up vector
				newUp = this->perpendicular();
			}
			else
			{
				newUp = up;
			}

			// Rotate up vector by random amount around this
			Quaternion q;
			q.FromAngleAxis( Radian(Math::UnitRandom() * Math::TWO_PI), *this );
			newUp = q * newUp;

			// Finally rotate this by given angle around randomised up
			q.FromAngleAxis( angle, newUp );
			return q * (*this);
		}

		/** Gets the shortest arc quaternion to rotate this vector to the destination
			vector.
		@remarks
			If you call this with a dest vector that is close to the inverse
			of this vector, we will rotate 180 degrees around the 'fallbackAxis'
			(if specified, or a generated axis if not) since in this case
			ANY axis of rotation is valid.
		*/
		Quaternion getRotationTo(const Vector3& dest,
			const Vector3& fallbackAxis = Vector3::ZERO) const
		{
			// Based on Stan Melax's article in Game Programming Gems
			Quaternion q;
			// Copy, since cannot modify local
			Vector3 v0 = *this;
			Vector3 v1 = dest;
			v0.normalize();
			v1.normalize();

			Real d = v0.dotProduct(v1);
			// If dot == 1, vectors are the same
			if (d >= 1.0f)
			{
				return Quaternion::IDENTITY;
			}
			if (d < (1e-6f - 1.0f))
			{
				if (fallbackAxis != Vector3::ZERO)
				{
					// rotate 180 degrees about the fallback axis
					q.FromAngleAxis(Radian(Math::PI), fallbackAxis);
				}
				else
				{
					// Generate an axis
					Vector3 axis = Vector3::UNIT_X.crossProduct(*this);
					if (axis.isZeroLength()) // pick another if collinear
						axis = Vector3::UNIT_Y.crossProduct(*this);
					axis.normalize();
					q.FromAngleAxis(Radian(Math::PI), axis);
				}
			}
			else
			{
				Real s = Math::Sqrt( (1+d)*2 );
				Real invs = 1 / s;

				Vector3 c = v0.crossProduct(v1);

				q.x = c.x * invs;
				q.y = c.y * invs;
				q.z = c.z * invs;
				q.w = s * 0.5;
				q.normalize();
			}
			return q;
		}


		/** Returns true if this vector is zero length. */
		inline bool isZeroLength(void) const
		{
			Real sqlen = (x * x) + (y * y) + (z * z);
			return (sqlen < (1e-06 * 1e-06));
		}

		/** As normalise, except that this vector is unaffected and the
			normalized vector is returned as a copy. */
		inline Vector3 normalisedCopy(void) const
		{
			Vector3 ret = *this;
			ret.normalize();
			return ret;
		}

		/** Calculates a reflection vector to the plane with the given normal .
		@remarks 
			NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.
		*/
		inline Vector3 reflect(const Vector3& normal) const
		{
			return Vector3( *this - ( 2 * this->dotProduct(normal) * normal ) );
		}

		/** Returns whether this vector is within a positional tolerance
			of another vector.
		@param rhs 
			The vector to compare with
		@param tolerance 
			The amount that each element of the vector may vary by
			and still be considered equal
		*/
		inline bool positionEquals(const Vector3& rhs, Real tolerance = 1e-03) const
		{
			return Math::RealEqual(x, rhs.x, tolerance) &&
				Math::RealEqual(y, rhs.y, tolerance) &&
				Math::RealEqual(z, rhs.z, tolerance);
		}

		/** Returns whether this vector is within a positional tolerance
			of another vector, also take scale of the vectors into account.
		@param rhs 
			The vector to compare with
		@param tolerance 
			The amount (related to the scale of vectors) that distance
			of the vector may vary by and still be considered close
		*/
		inline bool positionCloses(const Vector3& rhs, Real tolerance = 1e-03f) const
		{
			return squaredDistance(rhs) <=
				(squaredLength() + rhs.squaredLength()) * tolerance;
		}

		/** Returns whether this vector is within a directional tolerance
			of another vector.
		@param rhs 
			The vector to compare with
		@param tolerance 
			The maximum angle by which the vectors may vary and
			still be considered equal
		@note 
			Both vectors should be normalized.
		*/
		inline bool directionEquals(const Vector3& rhs,const Radian& tolerance) const
		{
			Real dot = dotProduct(rhs);
			Radian angle = Math::ACos(dot);
			return Math::Abs(angle.valueRadians()) <= tolerance.valueRadians();
		}

		// special points
		static const Vector3 ZERO;
		static const Vector3 UNIT_X;
		static const Vector3 UNIT_Y;
		static const Vector3 UNIT_Z;
		static const Vector3 NEGATIVE_UNIT_X;
		static const Vector3 NEGATIVE_UNIT_Y;
		static const Vector3 NEGATIVE_UNIT_Z;
		static const Vector3 UNIT_SCALE;

		/** Function for writing to a stream.
		*/
		inline friend std::ostream& operator <<
			( std::ostream& o, const Vector3& v )
		{
			o << "Vector3(" << v.x << ", " << v.y << ", " << v.z << ")";
			return o;
		}
	};

}

#endif